Tubes or stick with S/S

I use a few different amps with my Klipschorns, from a 2.5 watt Miniwatt through to a 20 watt Weston Acoustics Troubadour. You won't need more than anything between those numbers with your Cornwalls.

@OP, 

I own the Primaluna Dialogue HP integrated.  It's great.  I do, however, think, you might want to try a SET amp.  You do not need much power to make those C-Walls sing.  I should know.  Why? Because I have Klipsch Forte IIIs (in addition to less efficient speakers) and they sound better with a SET amp than the Primaluna, in my room.   

You could start with a Dennis Had amp (find him on eBay--he's the former owner of Cary Audio).  Wolfe (above) has one.  https://www.ebay.com/itm/STEREO-TUBE-AMPLIFIER-INSPIRE-by-DENNIS-HAD-300B-TRIODE-SINGLE-ENDED-AMPLIFIER/153463991221?hash=item23bb2aabb5:g:j7sAAOSw~PVcwdjC

I built the Elekit 8600 300B amp recently reviewed in Stereophile.  In a few nights you can have SET nirvana for ~$2K--if you do all the upgrades.  https://www.stereophile.com/content/gramophone-dreams-27-elekit-tu-8600r-amplifier-kit

If i may butt in here for just a moment and derail this topic momentarily to ask a question because it has to do with tubes. I just switched out my Callia DAC for the MHDT Orchid which has a tube output. So far it sounds REAL good (not yet broken in) and i am happy i made the switch. Problem is, i do not have volume control or very little via Tidal. So, my question is, is it possible to use (temporarily) the callia which has volume control or say a Mojo DAC which also acts as a preamp without it bypassing the Orchid? And lastly, i was thinking about getting the Schiit Freya preamp, it has tubes so would that kill the hybrid sound i now have or enhance it? Any comments, good or not so good would be helpful...       

I’m Single-Ended Triode. I also like mechanical watches. I have a SS amp down below for the family system. Like a mechanical watch - it wins before turning it on. I am enjoying my wife coming up to my cave to hear the music she can’t hear on the SS. To be fair, I spent 10X as much on it. Just like my watches.

Edit - add:
@15W/channel - I am near field, but never go above 30% dial.  I have run Martin Logan 35XT and not Watkins gen four (wow).  No issues with power.  Pushing ribbon, I understand I need more power.  So not pushing ribbon.  

     As a lifelong user of class AB and recently class D  ss amplification mainly out of necessity with my multiple succession of inefficient Magnepan speakers, I'd recommend going for the Primaluna and tubes or even a SET, especially with your highly efficient Klipsch Cornwall IIIs. You'd still have the option of switching back to your ss McIntosh during the summer or whenever you desired.
     I owned a pair of the original very efficient Klipsch Heresy speakers in college 40 yrs ago and still regret not even contemplating driving them with tube amplification.  
     I didn't even realize until years later how spectacularly beautiful music can sound with good tube amps driving well matched speakers.  
       Ever since listening to my 1st high quality system about 35 yrs ago, I've considered tubes as having a certain mystique and, please excuse the oxymoron, a certain coolness.  I've since experienced several friend's tubed systems, always impressed with the sound performance but also with the tubes glowing in the darkness that, imho, just adds to the enjoyment of listening to good music well reproduced.

Tim